Edge anisotropy and the geometric perspective on flow networks

TL;DR

This paper introduces a geometric approach to spatial networks by defining edge anisotropy, which helps analyze flow structures in geophysical data beyond traditional topological methods.

Contribution

It presents a novel measure of edge anisotropy in spatial networks and demonstrates its usefulness in understanding flow geometries from observational data.

Findings

Edge anisotropy quantifies local flow directions.

It complements topological analysis of flow networks.

Useful for identifying flow structures in geophysical data.

Abstract

Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.